In this article, we study the magnetic Neumann Laplacian on a domain with a small hole. Our attention is focused on the description of holes, which do not change the spectrum drastically. Moreover, we show that the spectrum of the magnetic Neumann Laplacian converges in the sense of the Hausdorff distance to the spectrum of the original operator defined on the unperturbed domain.

中文翻译：

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带孔域上的磁诺依曼拉普拉斯算子

在本文中，我们研究了小孔域上的磁诺依曼拉普拉斯算子。我们的注意力集中在空穴的描述上，这不会极大地改变光谱。此外，我们表明磁诺依曼拉普拉斯算子的谱在豪斯多夫距离的意义上收敛于在未扰动域上定义的原始算子的谱。